It is a process of obtaining permission to perform some operation, or of granting/getting access to somewhere, to someone or to something (not only in terms of access to specific premises or to a person, but also access to information, functions, program objects, etc.).
It often follows authentication, and usually, in computing systems, it gives an authorized user the appropriate authorities corresponding with his role in the system and allows him to access and work with defined files, folders and system functions.
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